According to the Qur'an the dominion of the morality of Islam over the world is an obligation

In many verses of the Qur'an Allah promises the dominion of the
morality of Islam all overthe world. The promise of our All-Mighty
Lord is true and Allah never failsto keep His promise. Those who
believe in Allah also believe that Allah's promise will absolutely
come true. Because our All-Mighty Allah gives the news of the dominion
of the morality of Islam over the world and promises it, what befalls
to sincerebelievers is to pray for its realization by heart, demand it
and strive for it with all their might. Believing that morality of
Islam will reign and making effort for the realization of this blessed
event is obligatory for every Muslim who abides by the Qur'an. In one
verse our All-Mighty Allah says:
Allah has promised thoseof you who believe and do right actions that
He will make them successors in the land as He made those before them
successors, and willfirmly establish for them their religion with
which He is pleased and give them, in place of their fear, security.
'Theyworship Me, not associating anything with Me.' Any who are
unbelivers after that, such people are deviators. (Surat an-Nur, 55)
Some other verses in which Allah promises thedominion of the morality
of Islam over the world are as follows:
Allah has written, 'I will be victorious, I and and My Messengers.'
Allah is Most Strong, Almighty. (Surat al-Mujadala, 21)
They desire to extinguish Allah's Light with their mouths but Allah
will perfect His Light, though the unbelievers hate it. It is He Who
sent His Messenger with guidance and the Religion of Truth to exaltit
over every other religion, though the associaters hate it.
(Suratas-Saff, 8-9)
They desire to extinguish Allah's Light with their mouths. But Allah
refuses to do other than perfect His Light, even though the kafirun
detest it. It is He Who sent His Messenger with guidance and the
Religion of Truth to exaltit over every other deen,even though the
associaters detest it. (Surat a-Tawba, 32-33)
Allah confirms the Truth by His words, even though the evildoers hate
it. (Surah Yunus, 82)
Those before them plotted but all plotting belongs to Allah. He knows
what each self earns, and the unbelievers will soon know who has the
Ultimate Abode. (Surat ar-Ra'd, 42)
We destroyed generations before you when they did wrong. Their
Messengers brought them the clear signs, but they were never going to
have faith. That is how We repay evildoers. Then We appointed you
after them to be successors onthe earth so We might observe how you
would act. (Surah Yunus, 13-14)
That those people of pure natural belief in Allah who do not associate
any partners toHim will be the inheritors of this world is a divine
Law which is stressed in many verses of the Qur'an:
We wrote down in the Psalms, after the Reminder came: 'It is My
servants who are righteous who will inherit the earth.' (Surat
al-Anbiya, 105)
We will leave you the land to live in after them. That is the reward
of those who fear My station and fear My threat.' They asked for
Allah's victory, and everyobdurate tyrant failed. (Surah Ibrahim,
14-15)
Moses said to his people,'Seek help in Allah and be steadfast. The
earth belongs to Allah. He bequeathes it to any of His slaves He
wills. The successful outcome is forthose who fear [and respect
Allah].' They said,'We suffered harm before you came to us and after
you came to us.' He said, 'It may well be that your Lord is going to
destroy your enemy and make you the successors in the land so that He
can see how you behave.' (Surat al-A'raf, 128-129)
We destroyed generations before you when they did wrong. Their
Messengers brought them the clear signs, but they were never going to
have faith. That is how We repay evildoers. Then We appointed you
after them to be khalifs on theearth so We might observe how you would
act. (Surah Yunus, 13-14)
Rather We hurl the truth against falsehood and it cuts right through
it andit vanishes clean away! Woe without end for you for what you
portray! (Surat al-Anbiya, 18)