In a tweet, the President also accused the U.S deputy attorney general of pursuing a "witch hunt".
An obstruction of justice finding could form the basis for Trump's impeachment but such a step would face a steep hurdle because it would require approval by the US House of Representatives, which is controlled by Trump's fellow Republicans.
Trump's tweet was part of an early-morning tweetstorm in which he went after the Russian Federation investigations and the "Fake News Media". Mr Pence hired criminal lawyer Richard Cullen as special counsel Robert Mueller's investigation intensifies.
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But Constand's is the only criminal case against him as under United States statues of limitations. They also complained that prosecutors improperly struck blacks from the jury chosen in Pittsburgh.
However, it is likely that he was tweeting about Deputy Attorney General Rod Rosenstein, or Mueller who is examining whether the president obstructed justice by firing ex-FBI Director James Comey last month amid the ongoing Russian Federation investigation.
An hour after the "nice" tweet, Trump continued to reiterate his stance that the investigation was a farce, tweeting again that it was a "witch hunt".
The memo ordered transition team members "to preserve any physical and electronic records that may be related in any way to the subject matter of the pending investigations". In a letter to Trump, Sessions called for a "fresh start" at the Federal Bureau of Investigation and recommended Comey's removal.
Now, Mr Trump has suggested that he is indeed being investigated. A day later, Rosenstein appointed Mueller as special counsel.
His latest tweets follow a report this week in The Washington Post reported that special counsel Robert Mueller's investigation into Russia's role in the 2016 election is looking into whether the president attempted to obstruct justice.
On Thursday, Russian President Vladimir Putin said Mr Comey had presented no evidence to prove that Moscow meddled in the USA election, adding that Washington had tried to influence Russian elections "year after year".