Most Senate Democrats said Tuesday they want to work with Republicans on rewriting the tax code, but made clear they oppose tax cuts for high earners.

A letter signed by 45 of the 48 Senate Democratic caucus members called for a bipartisan solution to modernize the tax system, in turn improving wages and stimulating job growth.

But it came with a condition.

“Any tax reform effort should not benefit the wealthiest individuals, who have already seen outsized benefits from recent economic gains," said the letter, authored by Minority Leader Chuck Schumer, D-N.Y., and others. "Tax reform cannot be a cover story for delivering tax cuts to the wealthiest."

The letter comes as congressional Republicans turn next to tax reform after struggling to advance a bill to repeal and replace ObamaCare. Republicans, though, could clash with their Democratic colleagues over the tax cut warning.

House Speaker Paul Ryan, R-Wis., says he's not pressing for a large, deficit-financed tax measure. But keeping GOP promises for large rate cuts won't be easy under those conditions, given the difficulty in eliminating popular deductions and tax breaks.

GOP leaders also intend to reject another Democratic demand: advancing the measure under regular legislative procedures instead of through the planned fast-track path.

The Associated Press contributed to this report.