Although Kislyak told senators last week that he would convey their concerns to leaders in his capital, he was also firm that not much can be done.

"We live in the environment of the law — that the law decides on how things can be done and cannot be done in Russia on these issues," Kislyak told reporters after the closed-door meeting.

The ambassador, reiterating the rhetoric of the Russian government on the ban, said that the law "didn't appear from nowhere. It is because of concerns that were prevailing in Russia about the fate of a number of kids that were adopted here in the States."

The Russian government's stance is that the ban is in place because Americans have mistreated the adopted children. Observers, however, consider the ban to be retaliation for a U.S. law targeting human-rights violators in Russia. Enacted late last year, the law is named after Sergei Magnitsky, a Moscow lawyer who died in a Russian prison in 2009 after he implicated top officials in a tax-fraud scam. The law denies visas to Russians implicated in the Magnitsky case and accused of human-rights violations, and it freezes their assets in the United States.

Russia's measure is named after Dima Yakovlev, a boy who died after his adoptive American parents left him in a locked car in a parking lot for hours on a hot day in Virginia. In addition to the adoption ban, the law sanctions U.S. citizens involved in human-rights violations against Russian citizens and suspends the activities of nonprofit organizations in Russia that receive money from the U.S.

But the ban, which went into effect on Jan. 1, has left hundreds of American families stuck in the middle of the adoption process, and members of Congress are trying to find a way to have their cases resolved. "Let's try to find some opening that allows these adoptions to be completed," said Blunt, who has been tackling this issue with Landrieu, the leader on adoption issues in Congress.

Also attending the meeting organized by Landrieu were Sens. John Bozeman, R-Ark.; Maria Cantwell, D-Wash.; Robert Casey, D-Pa.; Amy Klobuchar, D-Minn.; Claire McCaskill, D-Mo.; Jack Reed, D-R.I.; Sheldon Whitehouse, D-R.I., and Roger Wicker, R-Miss.

For Landrieu, the matter is personal. Her husband was adopted from an orphanage in Ireland when he was 5, and she is also the mother of two domestically adopted children. Landrieu says that because she has firsthand experience with "the miracle of adoption," she is all the more passionate about making sure that others can experience it as well. To that end, Landrieu has been appealing to the Russian government since the ban was put in place about "finding a way to continue to process the cases of children — there are about 500 or less out of thousands in the pipeline that have already been matched with their parents."