Nationals of countries that cut diplomatic ties with Qatar this week are free to remain in the Gulf state in line with existing regulations, according to the interior ministry.
The statement on Sunday, carried by Qatar's state news agency, said there was no change in policy towards the nationals of "brotherly and friendly countries, which cut or reduced diplomatic relations following the malicious and hostile campaigns against Qatar".
Saudi Arabia, the United Arab Emirates, Bahrain and Egypt have accused Qatar of supporting "terrorism".
Qatar strongly rejects the allegations and has said it is open to talks on ending the dispute, which also saw the three Gulf states order all Qatari citizens out of their countries within 14 days.
The crisis has raised deep concerns about instability in the region and, on Sunday, Kuwait's foreign minister said his country would continue efforts to mediate a solution to the crisis.
Qatar said late on Saturday it would not retaliate with such measures of its own.
The decision will come as a relief to the more than 11,000 people from Saudi Arabia, the UAE and Bahrain living in Qatar.
Concerns have been raised about the impact of these measures on people who live in all the countries affected.
"For potentially thousands of people across the Gulf, the effect of the steps imposed in the wake of this political dispute is suffering, heartbreak and fear," Amnesty International has said.
Saudi Arabia said on Sunday it was ordering "suitable measures" to help families with mixed citizenships, but provided few details.
Qatar's National Human Rights Committee dismissed the Saudi initiative to assist the families facing the prospect of being split up through deportation and expulsion as a "face-saving" exercise.
The NHRC said a hotline set up by Saudi Arabia, the UAE and Bahrain to helped mixed families was "too vague to have any practical impact" and was "void of a mechanism to be of assistance to those affected."
Source: Al Jazeera and news agencies