"while accusing" is correct and usable in written English
You can use it when you are describing an action (often an argument) that is happening at the same time as another action. For example: "She argued her case while accusing him of lying."
"The court accepted petitioner's factoid uncritically," they wrote, "all the while accusing the S.E.C. of paying inadequate attention to the empirical work before it, and of slipshod economic analysis in general".
Both candidates denied the other's accusations while accusing each other of waging a divisive campaign.
Has the city, while accusing the state, been shortchanging its own schools?
He noted the Russian President's "extraordinarily strong language" while accusing Turkey of acting as the "accomplices of terrorists".
While accusing federal prosecutors of not knowing "the difference between friendship and corruption," Menendez insisted he would be "vindicated".
He attacked his record on environmental and consumer protection while accusing him of being weak on foreign policy and crime.
Dealers acknowledged the system's flaw, but said they would never commit that offense, while accusing others of doing precisely that.
Obama, a natural unifier and conciliator, seems on the verge of running as a divisive populist while accusing Mitt Romney, his possible opponent, of being inauthentic.
And while accusing politicians of populist "election-year chaebol bashing," the conglomerates vowed to increase the number of new employees this year by 3.4 percent.
He declared it "my highest priority" to reverse those trends, while accusing other politicians of not only ignoring the problem but also making it worse.
In the end, he chose a single ex-beauty queen to run, while accusing other parties of favouring "smelly" and "badly dressed" candidates.
