The White House budget chief told Congress Monday that President Obama would like to free up some, but not all, of the leftover money from the Ebola fight to combat the Zika virus, which has been linked to birth defects in Latin America.

House Appropriations Committee Chairman Harold Rogers, Kentucky Republican, told the Office of Management Budget last week that about $2.7 billion of the $5.3 billion Congress set aside to combat Ebola hadn’t been used, so the administration should look to that money before asking for nearly $2 billion more to fight Zika, the latest global health scare.

OMB Director Shaun Donovan appeared ready to meet the chairman halfway Monday, saying Mr. Obama’s $1.9 billion request — formally submitted Monday — asks Congress to free up Ebola funding set aside for the State Department and U.S. Agency for International Development.

“While the Zika supplemental request reflects our best estimate given current information of potential needs to address Zika there remains significant uncertainty around the scope of the Zika challenges we will face. … Being able to use unplanned State/USAID Ebola funds will give us the flexibility to respond to Zika needs beyond what we have so far identified,” he said in a letter to Mr. Rogers.

Mr. Rogers’ figures last week put that amount at about $1.3 billion. However, the committee said $1.4 billion to the Health and Human Services Department also hasn’t been used, so there is still disagreement between the parties.