President Obama wisely began trying to improve the United States’ extremely sour relations with Latin America this week. He slightly eased the counterproductive embargo on Cuba, and in a visit to Mexico, he vowed to help confront the drug cartels. He also promised leaders at a regional summit a “new day” of practical cooperation in place of former President George W. Bush’s ideologically constricted policies.

Mr. Obama tackled the most neuralgic issue in hemispheric relations when he abandoned longstanding restrictions on the ability of Cuban-Americans to visit family members in Cuba and send them money. Cuba’s people have paid a high enough price for nearly three decades of repression and isolation imposed on them by Fidel Castro and his cronies.

Mr. Obama also allowed telecommunications companies to pursue licensing agreements in Cuba. Such deals are needed to pierce the wall of silence at the heart of the Cuban system by expanding access to cellphones and satellite television.

But these steps do not go far enough. We believe the economic embargo should be completely lifted.

President Raúl Castro responded to Mr. Obama’s overtures with a call for talks about “everything.” We hope the administration follows up and that Mr. Obama and Secretary of State Hillary Rodham Clinton continue to insist that Havana reciprocate by freeing political prisoners and respecting human rights.

Mr. Obama made a welcome commitment to help President Felipe Calderón of Mexico combat drug trafficking, which has caused a surge of attacks on both sides of the border. He acknowledged that America’s demand for illegal drugs fueled the trade and that its inability to stop the flow of weapons south fed the violence.

But he fell short on what’s required to fix the problem. During the 2008 campaign, Mr. Obama backed renewal of an assault weapons ban that expired in 2004. On Thursday, it was discouraging to hear him suggest that that would be politically impossible now because of opposition from the gun lobby. If he’s that timid, we do not see how he will fulfill his promise to Mr. Calderón to urge the Senate to ratify a long-stalled treaty aimed at curbing illegal arms trafficking.

The Bush administration left so much turmoil and resentment around the world that Mr. Obama might have been tempted to defer dealing with Latin America. We are encouraged that he seems prepared to take on the full plate of issues, including trade, immigration reform, economic recovery, poverty and climate change.

Whether Mr. Obama will win over Washington’s fiercest critics, like President Hugo Chávez of Venezuela, is unclear; the two men raised eyebrows on Friday by greeting each other warmly. But we suspect most Latin Americans will be willing to give him a chance. His challenge will be to stay seriously engaged — and to advance an even more effective agenda.