SACRAMENTO — Gov. Arnold Schwarzenegger on Monday proposed additional spending to cover medical services for 300,000 uninsured children, the latest glimpse of the state budget he will present Tuesday.

Schwarzenegger, speaking through a swollen upper lip from a weekend motorcycle accident, said the state can do a better job enrolling children already eligible for either of the two major public health care programs.

He said his budget for the 2006-07 fiscal year will include $72 million for state and county agencies to help locate and enroll children in the Medi-Cal and Healthy Families programs.

“We need to reach out and find those who are eligible but not enrolled,” Schwarzenegger said during a news conference at a health center for women and children in Los Angeles. “As you all know, there are over 400,000 children who are eligible for the healthy family program who are not enrolled yet. This is unacceptable for us.”

The proposal is the latest glimpse at provisions expected to be included in his budget. Schwarzenegger previously proposed spending about $4 billion more on education and freezing fee hikes for university students.

Last week, he proposed a $68 billion bond that would become part of a $222.6 billion public works spending plan.

The governor on Monday said he will propose a $1.2 billion increase in funding for health and human services programs.

The modest investment in outreach programs he proposed is expected to add 300,000 children in one of the two state-sponsored health care programs over the next two years, said Sabrina Demayo Lockhart, a spokeswoman for the state Health and Human Services Agency.

Lockhart said details on how much the new enrollees would cost the state in medical care would be released as part of the budget on Tuesday.

Advocates for the poor were heartened by Schwarzenegger’s proposal to improve access to medical services for the state’s low-income children, but said more needs to be done.

“We’re certainly pleased with the investment. It’s badly needed,” said Robert K. Ross, president and chief executive of the nonprofit California Endowment, which seeks to improve access to health care. “But it falls short of the vision that every child has access to quality care.”

Recent studies commissioned by the California Endowment found that it would cost the state $300 million to $400 million annually to provide care for all children, he said.