They argue that governments and the World Health Organisation should not repeat the early missteps of the COVID-19 pandemic that delayed the detection of cases, helping the virus spread.
While monkeypox is not as transmissible or dangerous as COVID-19, these scientists say, there needs to be clearer guidance on how a person infected with monkeypox should isolate, more explicit advice on how to protect people who are at risk, and improved testing and contact tracing.
"If this becomes endemic (in more countries), we will have another nasty disease and many difficult decisions to take," said Isabelle Eckerle, a professor at the Geneva Centre for Emerging Viral Diseases in Switzerland.
The WHO is considering whether the outbreak should be assessed as a potential public health emergency of international concern (PHEIC), an official told Reuters.
A WHO determination that an outbreak constitutes a global health emergency - as it did with COVID-19 or Ebola - would help accelerate research and funding to contain a disease.
"It is always under consideration, but no emergency committee as yet (on monkeypox)," Mike Ryan, director of the WHO's health emergencies program, said on the sidelines of the agency's annual meeting in Geneva.
However, experts say it is unlikely the WHO would reach such a conclusion soon, because monkeypox is a known threat the world has tools to fight.
Discussing whether to set up an emergency committee, the body that recommends declaring a PHEIC, is just part of the agency's routine response, WHO officials said.
Eckerle called for the WHO to encourage countries to put more co-ordinated and stringent isolation measures in place even without an emergency declaration.
She worries that talk of the virus being mild, as well as the availability of vaccines and treatments in some countries, "potentially leads to lazy behaviour from public health authorities".
More than 300 suspected and confirmed cases of monkeypox, a usually mild illness that spreads through close contact, causing flu-like symptoms and a distinctive rash, have been reported this month.
Most have been in Europe rather than in the Central and West African countries where the virus is endemic. No deaths have been reported in the current outbreak.
However, global health officials have expressed alarm over the growing outbreak in non-endemic countries. The WHO has said it expects numbers to rise as surveillance increases.
