Republican leaders in the House of Representatives, hoping to pass a measure before the November elections to improve legal immigration, are pushing for a vote this week on a bill that would increase the number of permanent resident visas for foreigners graduating from American universities with advanced degrees in science and technology.

The largely partisan bill was introduced on Tuesday by Representative Lamar Smith of Texas, the Republican chairman of the House Judiciary Committee. It would allocate up to 55,000 visas, known as green cards, each year to graduates with master’s or doctoral degrees from American universities, by means of a trade-off. The bill would abolish a lottery run each year that distributes the same number of green cards randomly to applicants from countries that do not have large immigrant populations in the United States.

The nearly 50 other sponsors of Mr. Smith’s bill include only one Democrat — Representative Henry Cuellar of Texas. Mr. Smith and Representative Eric Cantor of Virginia, the majority leader, have said the House will vote on Thursday.

A partisan fight broke out over Mr. Smith’s approach, which would not increase the overall number of green cards issued annually. On Friday Representative Zoe Lofgren of California, a Democrat whose district is home to many technology companies, introduced a measure that would create 50,000 new green cards for advanced graduates in the so-called STEM fields: science, technology, engineering and mathematics. That bill would not reduce the visas available to the lottery.