"The Government has initiated several steps to tackle Naxalism and terrorism but much more needs to be done and in this regard I need to meet chiefs of state ATS, Intelligence, Special Operations and law and judiciary departments," he said.
At the same time "improving service delivery and enforcing the rule of law" are also among top priorities, the 1977-batch IPS officer said.
"I will continue to initiate new steps towards improving the system," he added.
The new DGP said there was room for improvement in many areas, including investigation methods. "Taking new steps and improving existing system are not easy jobs but I will try to bring improvement which may not yield fruits in short-term but will certainly pay dividends in long-term."
While coastal security has been strengthened after the 2008 Mumbai terror attacks, there was scope for further improvement, said Dayal, a former Police Commissioner of the city.
On the charge that police often dilly-dallies when it comes to probing high profile cases, Dayal denied it, saying the force takes every case very seriously.
Asked specifically about the disproportionate assets case against former Mumbai Congress chief Kripashankar Singh, he said, "I had gone through the investigation (as ACB chief). It is wrong to say the police didn't probe the matter well." He said the ACB had submitted a report on Kripashankar's case to the Bombay High Court, which ordered the agency to probe the matter and later asked Mumbai Police to lodge an FIR against the Congress leader.