WASHINGTON — Gov. Rick Perry will travel to Dallas today to meet President Barack Obama at a round-table discussion with other leaders about the surge of unaccompanied, undocumented children crossing the U.S.- Mexican border.After a week of exchanges on whether the two would meet while the president was in the state, late White House senior adviser Valerie Jarrett wrote to Perry late Monday to extend an invitation to join the Dallas discussion.“The president would welcome a meeting with you while he is in Texas,” Jarrett wrote to Perry.Obama’s trip is primarily for Democratic fundraisers in Dallas on Wednesday and Austin on Thursday.On Thursday morning, he is scheduled to talk about the economy at mid-day at the Paramount Theater in Austin, a few blocks from Perry’s Capitol office.Perry earlier dismissed an invitation to meet Obama on the tarmac in Austin. He instead suggested a private meeting on the surge of illegal border crossings, according to the Austin American-Statesman.On Tuesday in an email to Bloomberg, Lucy Nashed, a Perry spokeswoman, said: “Governor Perry is pleased that President Obama has accepted his invitation to discuss the humanitarian and national security crises along our southern border, and he looks forward to meeting with the president tomorrow.”The round-table discussion in Dallas will include faith leaders and state and local officials to discuss the influx and how best to contain it.On Tuesday, Obama asked Congress to approve $3.7 billion to contain the surge of immigrants. More than 52,000 unaccompanied children arrived at the U.S.-Mexico border from Oct. 1 through June 15, about double the total in a similar period a year earlier, U.S. Customs and Border Protection reported. Most of the children are smuggled through Central America and Mexico, according to the White House.Perry, a potential Republican candidate for president in 2016, has said he’s warned the Obama administration for more than two years about unaccompanied children showing up at the border.“I don’t believe he particularly cares whether or not the border of the United States is secure,” Perry said July 6 on ABC’s This Week.