WASHINGTON — Thousands more children would eat lunches and dinners at school and all school food would become more nutritious under a bill President Obama signed into law Monday, part of an administration-wide effort to combat childhood obesity.

“At a very basic level, this act is about doing what’s right for our children,” Obama said before signing the bill. The ceremony was moved from the White House, where most signings are held, to an elementary school in the District of Columbia to underscore the point.

Besides Obama, the bill also was a priority for his wife, Michelle, who launched a national campaign this year against childhood obesity.

“We can all agree that in the wealthiest nation on earth, all children should have the basic nutrition they need to learn and grow and to pursue their dreams,” Mrs. Obama said. “Because in the end, nothing is more important than the health and well-being of our children. Nothing.”

The $4.5 billion measure increases the federal reimbursement for free school lunches by 6 cents a meal at a time when many school officials say they can’t afford to provide the meals. The bill will also expand access to free lunch programs and allow 20 million additional after-school meals to be served annually in all 50 states. Most states now only provide money for after-school snacks.

Many Republicans, including former Alaska Gov. Sarah Palin, have criticized the effort, saying the bill is too expensive and an example of government overreach.

Supporters say the law is needed to stem rising health care costs due to expanding American waistlines and to feed hungry children in tough economic times. Mrs. Obama cited a group of former generals and other military officials who have said unhealthy school lunches are a national security threat because weight problems are now the leading medical reason that recruits are rejected.