Standing within sight of Mexico, President Obama declared Tuesday that “we have strengthened border security beyond what many believed was possible,” in his latest attempt to rally support for a proposal that would create a path to citizenship for undocumented immigrants.

On his first trip to the U.S.-Mexico border as president, Obama attempted to blunt the conservative argument that the United States should secure its own borders before making any other changes to liberalize immigration law. Obama reeled off a series of statistics that he says prove U.S. borders are not plagued by illegal crossings and crimes, as many conservatives say.

“They wanted more agents at the border. Well, we now have more boots on the ground on the Southwest border than at any time in our history,” he said at the Chamizal National Memorial, a park here that is named after a 1963 agreement between the two countries and flies U.S. and Mexican flags.

Referring to conservative critics, he added, “The Border Patrol has 20,000 agents, more than twice as many as there were in 2004 . . . They wanted a fence. Well, the fence is now basically complete.”

The president accused Republicans of constantly looking to “move the goal posts” on what constitutes securing the border.

“Maybe they’ll need a moat,” he said, generating laughter from a crowd of more than 1,000. “Maybe they want alligators in the moat.”

Republicans say Obama is wrong in arguing that the border is secure. They cite a February report by the Government Accountability Office stating that only about 44 percent of the 2,000-mile U.S-Mexico border was under “operational control,” a measure of how easy it is to detect and then apprehend people illegally crossing into the United States.

“We hear from our constituents on a daily basis, and, while some progress has been made in some areas, they do not believe the border is secure,” Arizona Republican Sens. Jon Kyl and John McCain said in a statement after Obama’s speech.

The president’s speech was an attempt to balance two political groups that he must woo for his 2012 campaign. Obama pledged to Hispanic voters, who overwhelmingly backed him in 2008, that he would seek legislation that would make it easier for undocumented workers to become citizens.

At the same time, he wants to show political independents that he is committed to border security and that increased immigration affects their lives positively.

Obama did not lay out a specific bill for Congress to take up, but he did outline four principles: further increasing border enforcement funding if necessary, punishing companies that deliberately hire undocumented workers, streamlining the legal immigration process and creating a pathway to citizenship.

Senate Democrats announced late Tuesday that they would re-introduce the Dream Act, a bill that would provide a path to citizenship for some students. The measure passed the House last year, when it was controlled by Democrats, but died in the Senate.