WASHINGTON — House and Senate committees this week easily agreed to give President Obama fast-track authority to negotiate a sweeping trade accord with Pacific nations, but the package of bills intended to speed completion of the deal also imposes difficult burdens on its negotiators.

Senators demanded tough limits on currency manipulation by trading partners of the United States and placed restrictions on the import of products made with child labor. One provision would prohibit consideration of trade agreements with any country considered a violator of human-trafficking rules, a seemingly noncontroversial addition. But it could knock Malaysia from the deal, a 12-nation accord still being negotiated known as the Trans-Pacific Partnership.

Another provision would preclude trading partners from organizing boycotts, imposing sanctions or pressing divestment on Israel — popular here, less so in the Muslim countries in the deal.

As the trade promotion authority bills head to the House and Senate floors in coming weeks, skeptics and opponents have made it clear they are not finished.