Tens of thousands of people across Mexico have marched to protest against President Enrique Pena Nieto's proposal to recognise same-sex marriage in the traditionally conservative country.

Key points: Mexico's president has asked members of parliament to debate gay marriage

Mexico's president has asked members of parliament to debate gay marriage The Supreme Court has ruled laws restricting gay marriage are unconstitutional

The Supreme Court has ruled laws restricting gay marriage are unconstitutional The protest was organised by a coalition of Catholic and civil society groups

The marches were called by the National Front for the Family, a coalition of civil society organisations and various religious groups, and continued throughout the day from Mexico's far north to the Yucatan peninsula.

Same sex marriage is permitted in Mexico City, as well as in several states including Coahuila, Quintana Roo, Jalisco, Nayarit, Chihuahua and Sonora.

Pena Nieto has proposed changing the constitution to allow it nationally.

The embattled leader, who is grappling with discontent over a slowing economy, conflict of interest scandals, drug gang violence and a visit by US presidential hopeful Donald Trump that led to his finance minister's ouster, has opened himself to criticism by asking parliamentarians to debate gay marriage.

The National Front for the Family says it has gathered more than 100,000 signatures against same-sex marriage. ( AFP: Hector Guerrero )

"It's pulling on the noose," said Victor Sanchez, a sociologist at Colegio de la Frontera Norte in Tijuana.

"This comes as the Government is showing a certain sort of fragility in other areas ... and they're taking advantage of the moment."

Mr Pena Nieto says Congress should debate and settle the issue of gay marriage.

By midday on Saturday (local time), an estimated 40,000 people converged on the city of Queretaro in central Mexico, during a peaceful march through the city, one of the largest gatherings in the country, Civil Protection officers said.

"I think it was something unprecedented, the awakening of the society of Queretaro in defence of the family," said Jose Alcantara, an organiser with the National Front for the Family, adding the group had gathered more than 100,000 signatures against the proposal.

The protestors reject the president's proposal to allow same-sex marriage nationally. ( Reuters: Daniel Becerril )

Ary Campos Martinez, a spokesperson for Civil Protection in the city of Puebla in central Mexico, said officers had originally expected roughly 5,000 marchers, but were working to monitor a crowd of approximately 12,000 by midday.

In the northern city of Monterrey, others came to a central plaza in counter-protest of the marches to sing and read poetry.

"It's a discriminatory position and we hope it doesn't have success," said Jesus Gonzalez, 38, a human rights activist.

Mexico's Supreme Court said last year that laws restricting marriage to a man and woman were unconstitutional.

However, many state legislatures have not changed their statutes to comply, meaning couples must file legal challenges on a case-by-case basis to get married.

Gay marriage is still banned under local laws in many of Mexico's 31 states.

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Reuters