I would like to draw your attention to the current situation of hundreds of thousands of Daees in Pakistan known as the 'The Tablighi Jamaat'.Their faith is so strong that some of them even leave their wives, children and the comfort of their houses behind them in the name of Allah and dedicate their whole lives for the cause of Islam. They travel the world over for the cause of Islam just like you do.The only difference between you and them, however, is that they spread Islam among Muslims while you spread it among all (Muslims and Non-Muslims) openly. They believe that for them it has been 'forbidden' to give Da'wah openly to non-Muslims. Less than 2% percent of these Daees give Da'wah to non-Muslims (secretly and with fear). They literally go door-to-door the world over to as many Muslims as possible but they hardly ever knock at a non-believers door; nor do they ever address them in a common gathering like you do. You and I know, Al-hamdulillah, that they were Instructed by their Creator to invite everyone not just Muslims towards Him and in a manner which was most gracious. They are simply misled.I strongly feel that it is your duty as a follower of Mohammad (PBUH) to look into this matter and do something about it before its too late. This huge population of Daees of Pakistan have to be taught who needs Da'wah more and how to spread it.I think in the present global conditions of Islam, someone needs to issue a formal Fatwa which makes it farad for all Muslims to give Da'wah to non-Muslims. Give priority to non-Muslims when it comes to Da'wah.

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Know that al-Tabligh Jamaah is one of the groups that practise Da'wah to Islam. No one can deny its clear influence in the field of Da'wah, although there is disagreement among scholars and workers in the field of Da'wah concerning this group. Some support while others oppose the direction of such group.
Anyway, we think that the just position is: no one can completely accept or refuse all activities of al-Tabligh.
In other words, we are to accept what is proved by the Qur'an and Sunnah and vice versa.
Inviting non-Muslims is a collective duty for Muslims, i.e. if some Muslims do such activity the others will be free from responsibility. The Prophet (Sallallahu Alaihi wa Sallam) was used to ordering his delegations and expeditions to invite the others to Islam at first.
In Sahih al-Bukhari, the Prophet (Sallallahu Alaihi wa Sallam) said to 'Ali (Radiya Allahu Anhu): When the Prophet (Sallallahu Alaihi wa Sallam) sent him as a leader in the Ghazwa (expedition led by Prophet (Sallallahu Alaihi wa Sallam)) of Khaiber: "Go and take it easy until you arrive at their (non-Muslims) area, and then, invite them to Islam and tell them about Allah's right on them. By Allah! If Allah guides one man (to Islam) by your efforts, that will be better for you than the red camels" .
Also, in Sahih al-Bukhari that the Prophet (Sallallahu Alaihi wa Sallam) said to Mu'az when the Prophet (Sallallahu Alaihi wa Sallam) him sent to Yemen: "You will get to people who are followers of a Divine Book, so you have to invite them to the worship of Allah - The Great and Almighty - at first" .
It is narrated in al-Musnad of Imam Ahmad that A young Jewish boy used to serve the Prophet and he became sick. So the Prophet went to visit him. He sat near his head and asked him to embrace Islam. The boy looked at his father, who was sitting there; the latter told him to obey Abu-l-Qasim and the boy embraced Islam. The Prophet came out saying: "Praises be to Allah Who saved the boy from the Hell-fire." . This Hadith is also recorded in al-Bukhari .
Look! What great joy the Prophet (Sallallahu Alaihi wa Sallam) had due to the lad's embracing Islam.
Many Qur'anic verses and Prophetic Hadith confirm the obligation and excellence of inviting non-Muslims to Islam. The biographies of Prophet (Sallallahu Alaihi wa Sallam) and Messengers also bear more evidence in this context, since this is the first channel by which we can save them from the Hell-Fire, from misguidance to guidance. Life in this world will not be on the right way unless it is based on belief in Allah, and Islam is the only way of life and religion that Allah has chosen for people. So, it is our duty to invite others to Islam. Allah Says (interpretation of meaning): {… This day, I have chosen for you Islâm as your religion. …} [5:3].
In addition, inviting non-Muslims is the duty of the Muslim Ummah after Allah's Messenger (Sallallahu Alaihi wa Sallam). Then, non-Muslims will not have a pretext to claim that no one invited them.
Here, we reassure that inviting non-Muslims does not mean that there will be no problem if we neglect inviting Muslims and reminding them of Allah's Orders, since Allah Says (interpretation of meaning): {And remind (by preaching the Qur'ân, O Muhammad SAW) for verily, the reminding profits the believers.} [51: 55]. He also Says: {Therefore remind (men) in case the reminder profits (them). The reminder will be received by him who fears (Allâh),} [87: 9-10].
However, it is our duty to be just even with non-Muslim let alone with Muslims. Thus, we say that al-Tabligh group invites Muslims and non-Muslims.
Allah knows best.