Image copyright Reuters Image caption Mexico's foreign minister (R) did not hide his differences with US Secretary of State Rex Tillerson (L)

Mexico's foreign minister has expressed "irritation" to President Donald Trump's envoys about recent US policies towards its southern neighbour.

Luis Videgaray said he had told visiting US Secretary of State Rex Tillerson that Mexico was worried about respect for immigrants' rights.

Mr Tillerson said in Mexico City that "two strong sovereign countries" would have differences from time to time.

Relations between the neighbours are at their lowest point for decades.

A US plan, unveiled this week, to expel to Mexico all illegal immigrants found crossing the US border regardless of nationality has angered Mexicans most.

The body language at Thursday's meeting between the American and Mexican officials certainly did not suggest that ties had miraculously warmed in the space of a meal and a meeting, but the tone from both sides was more conciliatory than in recent weeks, the BBC's Will Grant reports from Mexico City.

'Hurt feelings'

Speaking first, Foreign Minister Videgaray said rebuilding the relationship would be a long process and would not be easy. He urged all concerned to "overcome the grievances and hurt feelings" to create a relationship based on trust and friendship.

"There's a concern among Mexicans, there's irritation [about] what has been perceived as policies that might be harmful for the Mexicans and for the Mexican industry," he said.

Secretary Tillerson spoke next, saying as a native Texan he had always considered Mexico a "very close neighbour", and echoing his counterpart's spirit of co-operation.

"In a relationship filled with vibrant colours," he said of the two nations, "there will always be differences".

Media playback is unsupported on your device Media caption Republican Senators have faced angry crowds at town hall meetings across the country.

Those differences were complicated further by the Trump administration's new guidelines on deportation of undocumented immigrants, especially those with criminal records.

It fell to Homeland Security Secretary John Kelly to reassure his hosts that there would be "no mass deportations" and no use of the US military in immigration enforcement.

That appeared to directly contradict what President Trump had said earlier in the day when he told a meeting of manufacturing CEOs that his administration had been getting "really bad dudes" out of the United States - before specifically stating that it was a "military operation".

Media playback is unsupported on your device Media caption US immigration raids leave many 'afraid to open the door'

Mr Tillerson and Mr Kelly later met Mexican President Enrique Pena Nieto behind closed doors before returning to Washington.

The Trump administration issued a new policy on Tuesday targeting millions of illegal immigrants for possible deportation, mirroring a previous executive order signed by the president.

Image copyright AP Image caption Mexicans deported from the US could be seen arriving at the airport in Mexico City on Thursday

The new policy, which seeks to step up enforcement of existing US immigration laws, widens the net on deportation and speeds up their removal.

It also calls for sending back to Mexico immigrants caught crossing the border illegally, irrespective of where they are from, and deporting anyone charged with, or convicted of, any crime.

President Trump has insisted that Mexico will pay billions for a wall along the US border, which prompted Mr Nieto to cancel a planned Washington visit late last month.

Both US and Mexican officials made no mention of Mr Trump's proposed wall at the news conference on Thursday.

Mr Trump has also ordered a report, due on Friday, listing all foreign aid the US provides to Mexico.

Media playback is unsupported on your device Media caption Where do America's undocumented immigrants live?

It is unclear why he requested the review, but its inclusion in Mr Trump's executive order on constructing a wall along the southern border suggests he may use it for leverage in negotiations with Mexico.

Mexican officials are also concerned about Mr Trump's pledge to renegotiate trade partnerships between the two countries.

The president has proposed to levy a 20% tax on Mexican imports to pay for a border wall.

Democratic senators urged Mr Tillerson and Mr Kelly to work through tensions with their Mexican counterparts on Thursday.

"We urge you to use your visit to disavow vitriolic rhetoric and forge a strong partnership based on mutual respect with the government of Mexico," the senators wrote in an open letter.