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"My thoughts are with the victims and their families. We stand with Belgium," Rasmussen said on Twitter.
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Deadly attacks on Tuesday at the Brussels airport and a metro station in the city are the latest in a string of attacks in Europe in recent years.
Cameron earlier said on Twitter he was "shocked and concerned" by the events in Brussels.
The blasts came days after the arrest of the top suspect in last year's Paris attacks, Salah Abdeslam, in Brussels.
"Out of precaution we are taking a number of additional measures in the Netherlands."
Jet Airways said it will soon be issuing a separate statement on the incident.
The metro operator later said the service was being closed down.
The alert level was raised from three to a maximum of four, and was applied across the country, Jambon's spokesman said, according to the Belga news agency.
Track the latest updates amid series of blasts in Brussels.
Questions have been raised about why the aircraft went ahead with its attempts to land when another jet heading for the same airport a short while earlier had diverted elsewhere because of the bad weather.