(CNN) A tense fight between House Democrats and President Donald Trump's administration over Cabinet officials resisting testifying on Capitol Hill escalated Wednesday when the House Homeland Security chairman warned he would not hesitate to issue a subpoena for Homeland Security Secretary Kirstjen Nielsen to appear before his panel .

Rep. Bennie Thompson, a Mississippi Democrat, sharply criticized Nielsen for refusing to testify February 6 though the Department of Homeland Security said she is open to other dates and that she had proposed alternate dates in February. On Tuesday night DHS Press Secretary Tyler Houlton strongly disputed that Nielsen had refused to testify , saying "she accepted the invitation and proposed alternative dates in February, as the proposed date of February 6 was unworkable."

Thompson said Wednesday that "I think not having any communications with the secretary is not where we need to be."

"Members of Congress need to hear from her. It's not an unusual request for the committee to hear from the head of the department," he added.

Nielsen's declining of the February 6 date follows several other Cabinet officials who have chosen not to voluntarily brief Congress. Treasury Secretary Steven Mnuchin declined a request from Ways and Means Chairman Richard Neal, a Massachusetts Democrat, to testify on January 24 about how the IRS was handling the partial government shutdown. Health and Human Services Secretary Alex Azar earlier this month declined a request to testify before the Energy and Commerce Committee. The refusals have left Democrats -- now in the majority in the House having promised to hold the Trump administration accountable -- fuming.

Asked if he's prepared to subpoena Nielsen, Thompson said: "I hope it doesn't come to that. I hope she sees the value of talking to the committee of jurisdiction for her agency. But if it comes to the fact that we can't get it any other way, it would not be a problem for me to do that."

He said he wants to hear from her by "the end of February."

CNN reached out to the Department of Homeland Security for comment on the threat of subpoena and a spokesman pointed to Tuesday's response to Thompson's letter. One DHS official said, "Why would you threaten to subpoena someone who has already agreed in writing to testify?"

In a letter obtained by CNN on Thursday, Nielsen told Thompson that she is "not available" to testify Tuesday, but "reiterates" that she can testify before his committee "as early as the week of February 18th."

A top administration official vigorously pushed back on Thompson's claim that Nielsen is refusing to appear in front of his committee, saying that DHS proposed other dates as early as the week of February 18 (Thompson have previously noted that Congress is scheduled to be on recess that week).

Nielsen said in the letter that she has "never refused to testify" before his committee. She also took issue with Thompson claiming that she canceled a meeting with him this week, saying, "We have no record of any meeting being confirmed for that date." She was out of town that day she said, and also offered to meet with him on Friday or can "provide additional options next week."

The administration official also pointed to the shutdown as a cause for delay: The staff necessary to prepare documents had not been working because of the shutdown and Thompson had requested thousands of pages of documents. The official said the Trump administration is working in good faith to fulfill oversight requests.

"We're trying to be nice, trying to be helpful. We have no problem with oversight," the official told CNN.

But the good feelings may be wearing off already, the official said, explaining that the back and forth playing out in the press may call for an amplified messaging response.

This story has been updated with additional developments Thursday.