MEXICO CITY, June 29 (Reuters) - Mexico"s foreign minister Marcelo Ebrard said on Tuesday the Mexican government had suggested to U.S. counterparts that travel restrictions on their shared border should change as vaccination programs advance. Restrictions on non-essential travel over the U.S.-Mexico border were first imposed in March 2020 in response to the COVID-19 pandemic and have been extended in 30-day increments. Border towns and businesses have been hit hard by a lack of cross-border traffic. "What Mexico is proposing is that as vaccinations move forward on both sides of the border the criteria changes for determining what restrictions and what activities are considered essential," said Ebrard, speaking as foreign ministers from the Group of 20 major economies met face-to-face on Tuesday for the first time in two years. Mexican President Andres Manuel Lopez Obrador said on Friday that his government will ask U.S. President Joe Biden, Vice President Kamala Harris, and California Governor Gavin Newsom to reopen the U.S.-Mexico border as soon as possible.