Democrats started hitting back at President Trump's tweets about North Korea on Sunday with tweets of their own questioning his judgment on matters of national security.

"If [Rex] Tillerson is wasting his time, it's only because his boss fails to understand the catastrophic consequences of war on Korean Peninsula," said Rep. Adam Schiff of California, the top Democrat on the House Intelligence Committee.

Schiff was responding to Trump's first wave of tweets on Sunday that said Secretary of State Tillerson should not concern himself with negotiations with North Korea over its ballistic missile development, and that he would take care of the situation.

"I told Rex Tillerson, our wonderful Secretary of State, that he is wasting his time trying to negotiate with Little Rocket Man," Trump tweeted.

David Axelrod, a senior adviser to former President Barack Obama, said Trump tweeted about North Korea to distract from the situation in Puerto Rico.

"Did @POTUS decide to undercut Tillerson on North Korea with Tweets just now to change subject from Puerto Rico story? It's the way he works," Axelrod tweeted. "Or maybe @POTUS just didn't have Rex's phone number so decided instead to have what should have been a private discussion in public!"

Sen. Ed Markey, D-Mass., jumped into the fray, tweeting out that Trump should drop the bad cop routine.

"Direct talks w/#NorthKorea are our best chance to freeze missile, #nuclear tests. Leave the bad cop routine in the movies, Mr. President," Markey said, who is a stalwart in the Senate on climate change and consumer rights.

He followed in another tweet saying Trump should focus on Puerto Rico and leave the situation in North Korea up to the diplomats.

"How about you do what has to be done to help #PuertoRico and let the diplomats negotiate in #NorthKorea to avoid a disaster there," Markey tweeted.

Still, most Democrats were still criticizing Trump over his 20 tweets from Saturday directed at critics of his response to the Puerto Rico hurricane disaster. Many in the leadership like House Democratic Whip Steny Hoyer, D-Md., had only caught up to the tweet storm of 24-hours ago, commenting on unrelated local topics by Sunday afternoon.

Senate Minority Leader Chuck Schumer, D-N.Y., was on the Sunday talk shows to respond to the GOP's tax reform proposal and the Puerto Rico tweetstorm. But that was just before Trump began sending tweets on North Korea and Tillerson.