White House counselor Kellyanne Conway on Sunday defended President Trump’s decision to lay blame for the deaths of two migrant children at the feet of Democrats, saying stronger border-security measures would deter attempts to cross illegally.

“The president does not want these children to come on this perilous journey to begin with,” Ms. Conway told CNN’s State of the Union.

Ms. Conway was defending a weekend tweet in which Mr. Trump faulted Democrats’ border policies as weak.

“Any deaths of children or others at the Border are strictly the fault of the Democrats and their pathetic immigration policies that allow people to make the long trek thinking they can enter our country illegally,” Mr. Trump tweeted. “They can’t. If we had a Wall, they wouldn’t even try!”

Some pundits said Mr. Trump’s Saturday tweet, the president’s first direct comments on the matter, suggested lack of empathy for the children.

An 8-year-old boy, Felipe Gomez Alonzo, died on Christmas Eve after six days in Border Patrol custody. He had been treated for a cold and fever at a hospital and was released, but was readmitted hours later — and died soon thereafter.

His mother in Guatemala said the boy’s father brought the child on the trip to the U.S. in the belief that gaining illegal entry would be easier with a child.

Earlier this month, a 7-year-old Guatemalan girl died after being arrested for crossing the border illegally with her father. Border Patrol agents twice managed to revive her after she fell ill, but she later suffered a heart attack and liver and respiratory failure at a hospital.

Ms. Conway said Democrats should have stayed in Washington to negotiate a way to put up barriers along the southern border, so the tide of migrants would be deterred.

“We simply cannot absorb all that,” Ms. Conway said.

Mr. Trump demanded $5 billion for his border wall. Democrats refused, resulting in a partial government shutdown that’s stretched across the holidays and could bleed into the new Congress.

“I think the president’s point is an important one,” Ms. Conway said. “He stayed in Washington to negotiate border security.”

• Dave Boyer contributed to this report.