Kramer, who is currently an affiliated senior fellow at Washington-based think tank, the McCain Institute for International Leadership, chose not to appear before the committee, FOX News broadcaster reported on Thursday, citing a law enforcement source.
Kramer testified before the committee in December in a closed-door session, indicated that he had some information about the dossier's sources and then received a subpoena.
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The compilation of memos with allegations of misconduct and conspiracy was made public by BuzzFeed news outlet in January last year, shortly before Trump's inauguration.
The White House has denounced all of the allegations in the dossier. Meanwhile, the intelligence committees both in US Senate and the US House of Representatives are looking into an alleged collusion between Trump's campaign and Moscow, which appears to be corroborated by the unverified dossier. A similar investigation is being led by the Special Counsel under the direction of former FBI Director Robert Mueller.
Moscow has repeatedly stressed that the allegations of collusion were false. Kremlin spokesman Dmitry Peskov called the dossier in particular "a forgery."