(Reuters) - Canada agreed with the United States on Thursday that slow-moving talks to update NAFTA should continue although they did not set a date for the next round, a senior official said in remarks casting further doubt on the chances of a deal this year.

Negotiations to modernize the North American Free Trade Agreement started last August and were initially scheduled to finish by the end of December.

That deadline has been extended several times as Canada and Mexico struggle to accommodate far-reaching U.S. demands for change such as a sunset clause that would allow one nation to pull out after five years. Canada and Mexico reject the idea.

U.S. officials had already made clear time was running out to secure a deal the current Congress could vote on. Democrats - who tend to be less enthusiastic about free trade than Republicans - are expected to make gains in midterm elections in November which could make passing a new NAFTA harder.

“We decided ... to continue our negotiations on NAFTA,” Canadian Foreign Minister Chrystia Freeland said in Washington after she met U.S. Trade Representative Robert Lighthizer.

“We will be working hard over the summer,” she said in remarks shown on Canadian television. “We didn’t set specific dates today. We talked about following up on setting up specific dates for meetings and that is what we are going to do.”

Although Lighthizer had initially pressed for a quick deal to avoid conflicting with a Mexican presidential election on July 1, Freeland said the three nations agreed they could continue the talks.

A Mexican source familiar with the negotiating process said officials were working to set up a fresh ministerial meeting soon after the election in Mexico.

Contentious issues were still unresolved and there was no situation visible in which Mexico would accept “for example, the sunset clause”, the source said.

Negotiating teams were still engaged in technical work and were on standby. “Nobody is depressed,” the source said.

Another challenge is the tariffs the United States imposed this month on Canadian and Mexican aluminum and steel.

Freeland said she had told Lighthizer Canada was resolute in its commitment to slapping retaliatory tariffs on U.S. goods on July 1. “We will not escalate and we will also not back down,” she said.