"By moving the U.S. embassy from Tel Aviv to Jerusalem, this legislation simply enforces current policy while reaffirming our commitment to Israel, one of our oldest and strongest allies," Heller said Tuesday. "Having spent time in Israel and seen firsthand the challenges that they face to ensure security and sovereignty, I believe the United States must stand firm in our commitment to the Israeli people."

Israel declared Jerusalem as its capital in 1950, but the U.S. has maintained its embassy in Tel Aviv. Palestinians have also claimed Jerusalem as their capital, and Obama administration officials have declined to say that Jerusalem is Israel's capital.

Heller's bill would say it is U.S. policy to recognize Jerusalem as Israel's capital. It also includes a sense of Congress that Jerusalem "must remain an undivided city" in which the rights of all ethnic and religious groups are protected.

That sense of Congress also encourages the president and secretary of state to "publicly affirm" that Jerusalem "must remain the undivided capital of the State of Israel."

A similar bill titled H.R. 104 was introduced in the House this past January by Rep. Scott GarrettErnest (Scott) Scott GarrettTrump taps nominee to lead Export-Import Bank Who has the edge for 2018: Republicans or Democrats? Rejected Trump nominee quietly hired by SEC: report MORE (R-N.J.).  Rep. Garrett's bill, like Senator Heller's, calls for the U.S. to recognize Jerusalem as Israel's capital city and to relocate the U.S. Embassy to Jerusalem, but with a deadline of no later than January 1, 2015.

The issue of Israel's capital became a sticky one for Democrats last fall, when they removed recognition of Jerusalem as the capital from their political platform. After that omission was noted by the press, convention chairman and Los Angeles Mayor Antonio Villaraigosa held a vote to put the statement back into the official platform.

Villaraigosa asked for a voice vote three times before deciding — some say incorrectly — that attendees supported putting the Jerusalem language back into the platform.

Sens. John CornynJohn CornynSenate moving ahead with border bill, despite Trump GOP senators introduce bill to prevent family separations at border Senate GOP tries to defuse Trump border crisis MORE (R-Texas), James InhofeJames (Jim) Mountain InhofeThe Hill's Morning Report — Sponsored by PhRMA — Trump caves under immense pressure — what now? Inhofe: Pruitt got 'wake-up call' after showing 'questionable judgment' GOP senators introduce bill to prevent family separations at border MORE (R-Okla.) and Mark KirkMark Steven KirkThis week: Trump heads to Capitol Hill Trump attending Senate GOP lunch Tuesday High stakes as Trump heads to Hill MORE (R-Ill.) are co-sponsors of the resolution.

- Updated at 3:30 p.m. Thursday