Currently, lobbyists representing foreign commercial interests register only with Congress, which requests minimal information, while those who represent foreign “principals” working for the benefit of foreign governments or political parties register with the Justice Department. The dual disclosure regimes create a huge gray area because in many countries, including Russia and Ukraine, the line between commercial and government interests is heavily blurred.

Mr. Grassley’s bill would also give the Justice Department more authority to demand information from lobbyists without resorting to a grand jury subpoena. Although the measure appears stalled for the moment, Christopher DeLacy, a Washington lawyer who has studied the FARA law, said “it’s a fairly safe bet that Congress is eventually going to take some sort of action.”

Unless his criminal charges are resolved through plea negotiations, Mr. Manafort’s coming trial will be the most public test of the law in recent history.

Coming on the heels of his conviction on financial fraud charges, the trial in federal court in the District of Columbia was set to examine charges that Mr. Manafort was the hidden hand behind a multiyear campaign to portray Viktor F. Yanukovych and the political forces behind him in Ukraine — all allies of President Vladimir V. Putin of Russia — as pro-Western backers of democratic and economic reforms. Mr. Manafort was paid more than $60 million by Ukrainian oligarchs to help orchestrate Mr. Yanukovych’s rise to Ukraine’s presidency and to maintain his grip on power for four years, before he was toppled and fled to Russia.

Prosecutors intended to show that Mr. Manafort hired lobbyists who met with members of Congress; helped organize meetings between top Ukrainian and American government officials, including a 2010 meeting in Washington between Mr. Yanukovych and President Barack Obama; and promoted the placement of articles and interviews in major American newspapers, including The New York Times.

The Manafort scandal already has touched a bevy of well-known lobbyists, lawyers and politicians who were paid millions to help him promote his Ukrainian clients. They include: Gregory B. Craig, Mr. Obama’s former White House counsel; Vin Weber, a Republican former congressman from Minnesota; Tony Podesta, a Washington lobbyist whose brother, John D. Podesta, headed Hillary Clinton’s 2016 presidential campaign; and Romano Prodi, a former prime minister of Italy. Several cases have been referred to federal prosecutors in New York.