A group of lawmakers from Museveni's ruling National Resistance Movement discussed the bill with the president and agreed in principle to sign the bill into law, chief whip Denis Hamson Obua said.
"Before that is done we also agree that the bill will be returned in order to facilitate the reinforcement and the strengthening of some provisions in line with our best practices," he told a news conference after the meeting.
Obua said Museveni would hold a meeting on Tuesday with parliament's legal and parliamentary affairs committee to draft the amendments.
The measure would impose the death penalty for so-called aggravated homosexuality, which includes having gay sex when HIV-positive, and 20-year sentences for "promoting" homosexuality.
Its passage last month with near unanimous support in parliament has already triggered a wave of arrests, evictions and mob attacks against LGBTQ Ugandans, members of the community say.
Museveni is a strong opponent of LGBTQ rights who last month called gay people "deviations from normal."
Human rights activists and the U.S. government say the bill is among the harshest pieces of legislation penalizing sexual minorities anywhere in the world.
The United Nations, European Union and a long list of corporate giants have condemned it.
Museveni faces a juggling act trying to keep lawmakers happy over legislation that has broad popular support while not antagonizing foreign donors who provide billions of dollars in aid each year.