Lawmakers have proposed a bill that would narrow the Obama administration’s room to negotiate new free-trade agreements, demanding that sensitive issues such as currency ma­nipu­la­tion be covered in future treaties and deepening congressional oversight of the process.

The legislation, introduced Tuesday by three of the top lawmakers on U.S. trade policy, would give the administration a green light to complete new trade pacts covering an important swath of Asia and Latin America and all of the European Union — the most significant such agreements in a generation.

But the bill also creates some difficult hurdles for the administration and sets up a potentially divisive debate over economic globalization and whether expanded trade agreements will produce more U.S. jobs or siphon them overseas.

The measure requires that future treaties set ground rules for how countries manage their currency values — a sensitive issue for any sovereign state that may be difficult to build into a trade agreement with countries as diverse as Japan and Peru. It also asks for limits on the role of state-owned enterprises, and it would allow any member of Congress to attend trade negotiating sessions.

The sponsors said the bill was crafted to help bring current European and Asian trade talks closer to completion while addressing some of the standing complaints about how trade pacts and globalization in general have affected the U.S. economy.

The bill “will make sure that these trade deals get done, and get done right,” said Senate Finance Committee Chairman Max Baucus (D-Mont.), who introduced the bill along with ranking Republican Orrin G. Hatch (R-Utah). Identical House legislation is sponsored by Ways and Means Committee Chairman Dave Camp (R-Mich.)

A brief statement from White House press secretary Jay Carney stopped short of endorsing the specifics of the bill but said its introduction was “an important step.”

Business groups have been urging such legislation for months and quickly endorsed the bill, while labor, environmental and other organizations skeptical of past trade agreements came out against it.

Significantly, Rep. Sander M. Levin (D-Mich.), the ranking Democrat on the House Ways and Means Committee, opposed the measure, evidence of the tough debate that may lie ahead.

The bill establishes “fast track” procedures so that trade agreements are subject only to a quick, up-or-down vote in Congress, with no amendments. Previous presidents have relied on fast-track authority to complete trade negotiations, and Obama has argued that he needs it, as well. The last such legislation was approved in 2002 on a narrow and largely partisan vote, something the Obama administration would prefer to avoid by convincing more Democrats that trade can be a net positive for the U.S. economy and the nation’s workers.

Levin, however, says the effects of globalization and past trade agreements have been so ambiguous — and so hard on some parts of the U.S. labor force — that Congress needs to set strict rules for any new treaties and should be more deeply involved while negotiations are underway. He says the bill does not go far enough in protecting the United States against unfair currency practices or the advantages held by state-supported companies in places such as Vietnam.

“We want expanded trade, but we want it shaped so the benefits are spread and accrue to workers,” Levin said. Among House Democrats, he said, there is “a strong feeling that as the pace of globalization accelerates, you need a more active shaping of the terms of trade.”

In recent years, concerns about the use of currency as a trade weapon have been focused on China, which maintains its renminbi at a level many analysts feel is undervalued and which makes the country’s exports cheaper. China is not part of the agreements under debate. But the administration hopes that the 12-nation Trans-Pacific Partnership in particular helps set global standards that China might eventually feel compelled to join.

Other countries in the region have also been suspected of using currency policy to achieve a trade advantage, and there has been pressure among U.S. lawmakers to address the problem on a more systematic basis.

The new bill marks the start of a larger discussion over trade policy. The “objectives” set out by Congress in the legislation would not be binding on the administration. But they would set some political limits on any treaty that the administration agrees to with its negotiating partners.

Depending on the final language of the bill, it could even strengthen the administration’s hand in future talks — allowing negotiators to present congressional demands on currency, for example, as make-or-break issues.