MEXICO CITY, Apr 6 (Reuters) - Mexico's president said on Wednesday the state should control around two-thirds of the national energy market within 18 months, doubling down on his pledge to give the public sector primacy in the dispute with foreign investors.

Mexico unveiled on Tuesday an agreement to buy $6 billion worth of assets from Spanish energy giant Iberdrola, and presented it as a "new nationalization" that would raise the market share of state-owned Comisión Federal de Electricidad (CFE) to 55.5%.

President Andrés Manuel López Obrador said that by the time his administration concludes on September 30, 2024, the CFE should have at least 65% of the energy market, with a maximum of 70% as new power plants come on line.

"We are going to keep fighting for Mexico," he told a press conference.

Lopez Obrador, a leftist politician who favors nationalization of resources, has been locked in disputes with investors over energy for years. Last year, this led to a formal trade complaint from the United States.

The United States and Canada, which quickly joined the complaint, claim that Lopez Obrador's energy policies have put their companies at a disadvantage. The president argues that previous Mexican governments manipulated the energy market in favor of private interests at the expense of the public.

Mexico faces potentially costly sanctions if the United States and Canada decide to convene -- and win -- a dispute resolution committee over its controversial energy measures.

That option has been open to both countries since October, and while Mexico says discussions to resolve the North American nations' concerns have progressed, frustration is mounting among U.S. companies.

Lopez Obrador says CFE should have at least 54% of the market.

However, his latest decisions suggest he wants to create as big a monopoly as possible and keep pressure on competitors until they sell, said Jorge Castañeda, Mexico's former foreign minister.

"That's the message he's sending to the Americans and Canadians," he said, arguing that, with the Iberdrola deal, Lopez Obrador was challenging both countries to escalate the trade dispute, with the idea that they wouldn't dare.

Given that months have passed without repercussions in the energy dispute, Castañeda said the Biden administration seemed reluctant to risk antagonizing López Obrador on trade, lest Mexico become uncooperative in curbing illegal immigration.

Meanwhile, by acquiring Iberdrola's assets, Lopez Obrador had bolstered the CFE with the use of cash, helping to offset the setback he suffered in Congress last year when he failed to get the votes needed to change the law to that end, he added.

Iberdrola shares rose 2.45% on Wednesday, while the Mexican peso fell around 1%, lagging against other currencies in the Americas.

Analysts said the peso's losses reflected concerns about the outlook for the U.S. economy, although some wondered whether the Iberdrola deal, which has capped a tumultuous chapter in relations between Lopez Obrador and the company, could also be weighing.

James Salazar, an analyst at CI Banco, said it was unlikely, as López Obrador's positions were well known in the market.

"The president sold it as a nationalization," he said. "But that's a political statement: it wasn't the case."

(Reporting by Dave Graham; additional reporting by Aida Pelaez-Fernandez; editing by Stephen Coates; Spanish editing by Flora Gomez)