Which takes priority: calling non-Muslims to Islam or calling non-committed Muslims to become religiously committed?

What appears to be the case based on the general meaning of the shar‘i evidence concerning that is that calling people to Allah, may He be exalted, is a communal obligation (fard kifaayah) upon the ummah and it is an individual obligation (fard ‘ayn) upon every Muslim, according to his level of ability and knowledge. The Prophet (blessings and peace of Allah be upon him) said: “Convey from me, even if it is only one verse.”

Narrated by al-Bukhari, 3461 

Ibn Katheer (may Allah have mercy on him) said, in his commentary on the first in which Allah, may He be exalted, says (interpretation of the meaning): “Let there arise out of you a group of people inviting to all that is good (Islam), enjoining Al-Ma‘roof (i.e. Islamic Monotheism and all that Islam orders one to do) and forbidding Al-Munkar (polytheism and disbelief and all that Islam has forbidden). And it is they who are the successful” [Aal ‘Imraan 3:104]: 

What is meant by this verse is that there should be a group of this ummah who carry out this mission; however, that is also obligatory upon every individual of the ummah according to his means, as it is proven in Saheeh Muslim that Abu Hurayrah said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever among you sees an evil action, then let him change it with his hand [by taking action]; if he cannot, then with his tongue [by speaking out]; and if he cannot, then with his heart – and that is the weakest of faith.” According to another version: “Beyond that there is not even a mustard seed’s worth of faith.” 

End quote from Tafseer Ibn Katheer, 2/78 

Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him) said: 

The evidence from the Qur’an and Sunnah indicates that it is obligatory to call people to Allah, may He be glorified and exalted, and that this is one of the obligatory duties. The evidence for that is abundant, such as the verses in which Allah, may He be glorified, says (interpretation of the meaning):

“Let there arise out of you a group of people inviting to all that is good (Islam), enjoining Al-Ma‘roof (i.e. Islamic Monotheism and all that Islam orders one to do) and forbidding Al-Munkar (polytheism and disbelief and all that Islam has forbidden). And it is they who are the successful”

[Aal ‘Imraan 3:104]

“Invite (mankind, O Muhammad SAW) to the Way of your Lord (i.e. Islam) with wisdom (i.e. with the Divine Inspiration and the Quran) and fair preaching, and argue with them in a way that is better”

[an-Nahl 16:125]

“and invite (men) to (believe in) your Lord, and be not of Al-Mushrikoon (those who associate partners with Allah”

[al-Qasas 28:87]

“Say (O Muhammad SAW): "This is my way; I invite unto Allah (i.e. to the Oneness of Allah – Islamic Monotheism) with sure knowledge, I and whosoever follows me (also must invite others to Allah i.e., to the Oneness of Allah – Islamic Monotheism) with sure knowledge”

[Yoosuf 12:108]. 

So Allah, may He be glorified, has explained that the followers of the Messenger (blessings and peace of Allah be upon him) are those who call people to Allah; they are the people of insight. What is required, as is well known, is to follow him and adhere to his way, as Allah, may He be exalted, says (interpretation of the meaning):

“Indeed in the Messenger of Allah (Muhammad SAW) you have a good example to follow for him who hopes in (the Meeting with) Allah and the Last Day and remembers Allah much”

[al-Ahzaab 33:21].

The scholars have clearly stated that calling people to Allah, may He be exalted, is a communal obligation (fard kifaayah) with regard to the regions in which the callers live, for every region and area needs the da‘wah (call) and needs people who are active in this field. So it is a communal obligation; if sufficient numbers of people undertake it, the duty is waived from the others and for the others da‘wah becomes a confirmed Sunnah (Sunnah mu’akkadah) and a great righteous deed. 

But if the people of a specific area or region do not undertake da‘wah, the burden of sin is incurred by all of them, and it becomes obligatory for all of them; each person must undertake to call people to Islam, according to his ability. However, generally speaking, with regard to every country, what is required is for there to be a group that is devoted to the mission of calling people to Allah, may He be glorified and exalted, throughout the world, to convey the message of Allah and to explain the command of Allah by all possible means, because the Messenger (blessings and peace of Allah be upon him) sent out callers, and he sent letters to people and to kings and rulers, calling them to Allah, may He be glorified and exalted.

See: Majmoo‘ Fataawa Ibn Baaz, 1/330 

Secondly: 

There is no need at all for differences as to which work should take precedence: calling Muslims or calling non-Muslims. The one whom Allah enables to do any of that should go ahead with it. There are some Muslims who are good at calling non-Muslims, because Allah has given them the ability to explain things clearly or to convince people easily, or He has enabled him to learn the language of the non-Muslims whom he is calling, or because of the nature of his work, as there are many non-Muslims with him, or because he travels to their country or because he has a neighbour who is a non-Muslim, and so on. 

In such cases we say to the individual: Go ahead and call these people with wisdom and beautiful preaching, with clear proof, and with patience in dealing with them. 

See also the answer to question no. 99976 for information on how to call these people. 

And there are some Muslims who are good at calling their fellow Muslims, because of some of the things that have been mentioned above; or because he does not have the patience to call non-Muslims; or because he has skills in convincing and debating in various issues and establishing clear proof; or because he is well versed in some branches of Islamic knowledge that may be needed more by one who calls Muslims than one who calls non-Muslims. 

The point of all this is to say that there is no need for disputes or arguments, let alone division, around this issue. Both are necessary according to sharee‘ah, and each person will be enabled to do that for which he was created. The one who finds that he has an interest and is able to work in either of the two fields should not denounce anyone who works in the other field, because both of them are good and are necessary, and neither takes precedence over the other at all. We do not know of any one among the early daa‘iyahs (callers) who said: We are going to refrain from calling the non-believers until we have set straight the Muslims’ affairs. When will that ever happen?! 

Moreover, we do not know of anyone who says that we should refrain from calling Muslims, teaching them and setting their affairs straight in order to focus on calling the non-Muslims and bringing them to Islam. 

There is no room for conflict in da‘wah; rather it is the task of every Muslim, each according to what he is able to do and what Allah has given him of knowledge, forbearance, wealth and so on. 

See also the answer to question no. 77579, 164443

And Allah knows best.