The president tried to clarify his approach to Iran and Israel, but ended up muddying the water.
Many details must still be hammered out, including the pace and extent of sanctions removal.
"Look, the president needs to sell this to the American people, and Congress needs to be involved," said Senator Bob Corker.
Convincing Congress to accept the Iran nuclear framework agreement will be a daunting political challenge for Obama.
Netanyahu has not yet publicly commented on the matter.
By playing nice on Iran, Russia hopes to strengthen its hand on Ukraine.
Iran's Foreign Minister Javad Zarif tweeted: "Found solutions, ready to start drafting immediately".
Six world powers and Iran struggled to conclude an outline accord on Tehran's nuclear program in the face of a U.S. threat to abandon the talks.
For days Iran, the United States, Britain, France, Germany, Russia and China have been trying to break an impasse.
The Congressional Black Caucus may decide whether Obama's critics nix a nuclear deal with Iran.
Iran has already destroyed its weapons-grade uranium and halted the Arak nuclear plant.
Major world powers have quietly begun talks on a U.N. Security Council resolution to lift U.N. sanctions on Iran.
The "open letter" to Tehran may raise laughs here, but it will make the Mullahs less likely to come to an agreement.
Iran's foreign minister on Thursday suggested that a 10-year freeze on some aspects of the country's nuclear program might be acceptable.
Ayatollah Ali Khamenei has responded to overtures from U.S. President Barack Obama amid nuclear talks with a secret dispatch, The Wall Street Journal reported Friday.
The conversion makes the nuclear material less suitable for building atomic bombs, a diplomatic source and a U.S. think-tank said on Monday.