More than 50,000 people have urged Barack Obama to escalate the diplomatic feud that led Moscow to propose a law barring Americans from adopting Russian children.
Two petitions on the White House website are asking for sanctions against Russian politicians who backed a bill that one of the documents says will "jeopardise lives and well-being of thousands of Russian orphans".
Moscow sees the ban on adoptions as retaliation for a US human rights law that allows the seizure of assets from Russian officials implicated in the 2009 death of a Russian lawyer.
Some Russian politicians denounced the petitions, saying any further action would cause tensions between the countries.
However a senior member of the Duma - Russia's lower parliamentary chamber - suggested there might still be a way for the measures to be softened.
One petition said Russian politicians "breached all imaginable boundaries of humanity, responsibility, or common sense and chose to jeopardise lives and well-being of thousands of Russian orphans".
The petitioners urged the president to "identify those involved in adopting such legislature responsible under the Magnitsky Act".
A second petition asks that the Magnitsky Act "be extended to supporters of this law in (the) Russian Duma".
According to White House rules, an official response will be issued if a petition reaches 25,000 signatures within 30 days. One already has more than 45,000 signatures, while the other has 6,000.
Russian deputy Irina Yarovaya, who heads the Duma's security committee, denounced the petitions.
Such initiatives "cross the limits of international law, of international relations and of a nation's sovereign rights", she said.
Another politician, Vyacheslav Nikonov, told Moscow Echo Radio that if Washington acted on the petitions, it could lead to "very serious diplomatic complications".
But deputy chairman of the Duma Sergei Zheleznya has hinted that the measures could be softened.
Between 2008 and 2011, American parents adopted 5,177 of the 14,660 Russian children adopted by foreigners.
The US human rights law has been dubbed the Magnitsky Act after Sergei Magnitsky, the lawyer who blew the whistle on what he said was a \$235m (£145m) police embezzlement scheme.
Moscow's proposed ban is unofficially called the Dima Yakovlev bill in memory of a Russian child who died of heat stroke while locked in a car by his adoptive US parent in the summer heat in 2008.