Sekulow was referring to a report in the Post this week that said Special Counsel Robert Mueller's investigation of Russian interference in November's presidential election was now also trying to determine whether Trump obstructed justice.
But Rosenstein could end up recusing himself, too, Justice officials say, in part because he played a role in President Donald Trump's firing of FBI Director James Comey.
While Mr Trump's tweets following the report appeared to confirm the investigation, Mr Sekulow lawyer said it only appeared that way because of the character limit on Twitter.
Also, it was Rosenstein who appointed Robert S. Mueller III as the special counsel to lead that investigation after Comey was sacked.
A lawyer for President Donald Trump said he is not under investigation, even though the president himself said he was.
One of Donald Trump's lawyers insisted on Sunday that the president was not under criminal investigation as part of the sweeping probe into Russia's alleged meddling in American elections, despite the United States leader's tweets angrily calling the whole saga a "distraction". "The Washington Post issued a story that had five anonymous sources, which they never identified what agencies those sources originated out of". Trump, a Republican, later said that he had the Russian Federation matter in mind when he fired Comey.
Trump advisers describe the president as increasingly angry over the investigation, yelling at television sets carrying coverage and insisting he is the target of a conspiracy.
"There should be no confusion", Sekulow added.
58 people missing and presumed dead in London fire
The long-term consequences need to be addressed now, they said . "No one local authority would be able to cope", he added. There were also scuffles and anger at police when Prime Minister Theresa May tried to visit the tower.
Rosenstein was also the author of a letter in May to Trump criticizing the performance of FBI Director James Comey.
"He was fully aware that if, in fact, he took this action, he would see a lengthening or could see a lengthening of the process", Sekulow said.
While aides have advised Trump to stay off Twitter, the president continued to weigh in Sunday as he spent the weekend at Camp David, the government-owned presidential retreat in Maryland. By that afternoon, Trump was re-litigating the 2016 election; "Why is that Hillary Clintons family and Dems dealings with Russian Federation are not looked at, but my non-dealings are? he tweeted".
Although the president is unlikely to be indicted if the Mueller's investigation finds any criminal wrongdoing, Mueller's findings could lead to calls for impeachment in Congress, where a few Democrats already are pushing for impeachment.
Until Trump's Friday-morning Twitter burst, only the Washington Post's sources had indicated that Trump was being investigated for possible obstruction of justice.
Mueller's move came after Comey said in his June 8 testimony to the Senate Intelligence Committee that he intentionally handed over his memos, detailing each conversation he had with the president, over to Mueller.
ABC said Mr Rosenstein told Associate Attorney-General Rachel Brand she would have authority over the probe if he were to step aside.
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