The Israeli government on Thursday barred Tlaib and Omar from entering the country over their support for an initiative to boycott Israel. US President Donald Trump tweeted it would show "great weakness" if the pair were allowed entry.
Both women were due to visit the occupied West Bank and East Jerusalem next week, reports say.
Omar described Israel's move as "an insult to democratic values and a chilling response to a visit by government officials from an allied nation".
Tlaib, however, sent a letter addressed to Israel's Interior Minister Aryeh Deri in which she sought a humanitarian permit to enter the country and promised to respect any restrictions imposed by authorities, Efe news reported.
She also promised not to promote the Boycott, Divestment and Sanctions (BDS) movement which aims to end international support for Israel because of its policies towards Palestin as well as its continued construction of West Bank settlements, considered a violation of international law.
On Friday, granting Tlaib the permission to visit Israel, the Interior Ministry said in a statement: "Tlaib sent a letter last (Thursday) night to Minister Dery, in which she promised to hold to Israel's requests, respect the limitations put on her for the visit and also affirmed that she would not promote the boycott against Israel during her visit.
Tlaib had asked Deri for access so that she could visit her relatives, "and specifically my grandmother, who is in her 90s and lives in Beit Ur al-Fouqa. This could be my last opportunity to see her".
Trump had earlier had taken to Twitter to urge that the two lawmakers be blocked from visiting, adding that "they hate Israel and all Jewish people, and there is nothing that can be said or done to change their minds".
Omar and Tlaib have been criticized for their stance on Israel - but have denied charges of being anti-Semitic. They have repeatedly supported the BDS, which gives the country legal grounds to ban their entrance under a law issued in 2017.
Israeli Prime Minister Benjamin Netanyahu said that "the detailed itinerary both congresswomen have makes it clear that they are aiming at harming the country".
"They planned a visit whose sole objective is to strengthen the boycott against us and deny Israel's legitimacy," he added.
They did not ask for meetings with any Israeli official or opposition leader, Netanyahu said, pointing out that the trip was sponsored by the Palestinian organization of Miftah.
Palestine Liberation Organization, meanwhile, considered the entry ban as a "scandalous act of hostility against the US people and their representatives".
( With inputs from IANS )