* Talks to modernize 1994 trade deal going slowly

* Elections loom in Mexico, U.S. this year

* Trump tariff proposal ratchets up pressure (Recasts with Lighthizer comments seeking deal "in principle," adds Guajardo, Freeland comments)

By Lesley Wroughton and Sharay Angulo

MEXICO CITY, March 5 (Reuters) - Mexican and U.S. officials pushed on Monday to speed up NAFTA negotiations, with the United States floating the idea of reaching an agreement "in principle" in coming weeks to avoid political headwinds later this year.

U.S. Trade Representative Robert Lighthizer, showing impatience at the slow pace of the talks, said Mexico's presidential election and the looming expiry of a congressional negotiating authorization in July put the onus on the United States, Mexico and Canada to come up with a plan soon.

"We probably have a month, or a month and a half, or something to get an agreement in principle," Lighthizer told reporters at the conclusion of a seventh round of talks to overhaul the North American Free Trade Agreement in Mexico City.

He was speaking after meeting Mexican Economy Minister Ildefonso Guajardo and Canadian Foreign Minister Chrystia Freeland for a joint event marked by a more cordial mood than in previous rounds, despite major disagreements over U.S. President Donald Trump's plan to impose steel tariffs.

Trump has threatened to dump NAFTA unless it boosts U.S. manufacturing and employment, arguing the 1994 accord has caused the migration of jobs and factories southward to lower-cost Mexico.

Guajardo told reporters the three countries aimed to hold lower-level discussions on NAFTA over the next five weeks before an eighth round, probably in early April.

During that period, he and his two counterparts also aimed to meet to narrow differences on the most complex issues in the talks, which include agreeing on new auto content rules, a dispute-resolution mechanism and agricultural market access.

Lighthizer said time to rework the deal was running "very short" and again raised the possibility of the United States pursuing bilateral deals with its partners - albeit stressing that his government would prefer a three-way agreement.

He said the United States was making more headway with its southern neighbor than with Canada.

Freeland declined to give details on a prospective timeline for the next round and said alongside Lighthizer that Trump's plan to impose a 25 percent tariff on steel imports and a 10 percent tariff on aluminum imports was "unacceptable".

The U.S. trade promotion authority, or TPA, is authorized by Congress and is needed to implement legislation for new trade agreements such as the renegotiation of NAFTA. The TPA expires on July 1 and analysts expect it to be extended.