Merkel gave an interview to publishing group Funke Mediengruppe, published on Thursday
There are “unfortunately very different levels of laws in individual states,” Merkel said.
“The states should therefore work to reach the same security level, because North Rhine-Westphalia for example practices, regrettably, no random police checks,” she continued.
“It would be very sensible to conduct these identity checks without suspicion in all states.”
Merkel further added that preventative surveillance measures by the police, for example monitoring potential dangerous suspects, is important.
“This is indeed done in Bavaria, but not in Berlin or NRW,” she said.
“We will never resign ourselves to terrorism,” Merkel added.
“We know that we are threatened, as are many other countries, and are doing everything in our power to ensure our citizens have security in freedom - including a close coordination between federal and state governments.”
She added that security authorities have been given more personnel as well as resources, and that “where necessary, we also adapt the laws.”
Merkel gave the interview amid ongoing investigations in North Rhine-Westphalia into the explosive attack against the Borussia Dortmund team bus on Tuesday. Investigators have said they suspect a terrorist background to the attack in which one player and one police officer were injured before a Champions League match against AS Monaco.
A suspected member of Isis was initially detained in connection with the attack, but federal prosecutors overseeing the investigation said on Thursday that they had found no evidence that he had participated in the explosions.
Officials have not yet ruled out other possible motives for the attack, such as violent football fans, right-wing extremists or extortionists.
Security officials came in for criticism after the Berlin terrorist attack in December in which a Tunisian Isis supporter drove a truck into a crowded Christmas market and killed 12 people.
The perpetrator had already been in the crosshairs of security services and should long ago have been sent back to Tunisia, which for months refused to take him.
Germany must 'take action' against refugees who abuse aid
The Chancellor also conceded in the interview that there could be some dangerous individuals among the more than one million refugees who have come to the country over the past two years.
"There is no dispute that among the many people who have come to our country searching for refuge, there are also people who are in the sights of our security agencies," she said.
"Therefore we owe it to the many respectable refugees, like all of us, to doggedly take action against all those who despicably abuse our willingness to help."
Merkel also said that one should not forget "that our country was already in the sights of Islamist terrorism before the many refugees came to us."