"We're in the decisive moment of the crisis, the number [of deaths] will continue rising," he told a news conference.
Mr Cordova said nearly 2,000 people had been hospitalised since the first case of swine flu was reported on 13 April, but half had now been allowed home.
Schools nationwide are to remain closed until 6 May as the country attempts to grapple with the outbreak.
As Mr Cordova spoke, Mexico City - where the outbreak is centred - was rocked by a 5.6-magnitude earthquake. It shook tall buildings and led to evacuations, but there have been no reports of damage or injuries.
The US confirmed a further 20 cases of swine flu in New York - bringing the current number of cases in the country to 40.
SPREAD OF VIRUS
Mexico: 26 confirmed cases (Mexico puts suspected deaths at 149)
United States: 40 confirmed cases
Canada: 6 confirmed cases
Spain: 1 confirmed case
UK: Scotland says tests confirm 2 cases
Israel, Brazil, Guatemala, Peru, Australia and New Zealand: Suspected cases being tested
The rise was entirely due to further testing of pupils at a school in Queens, Dr Richard Besser, acting director of the US Centers of Disease Control and Prevention (CDC), said.
Of the other cases reported - in Ohio, Kansas, Texas and California - only one person had been hospitalised and all had recovered, he added.
However, he warned that a new US travel advisory was being prepared suggesting "non-essential travel to Mexico be avoided".
Earlier, US Secretary of State Hillary Clinton urged "caution" for US nationals planning to visit Mexico, saying officials were taking the issue "very seriously".
EU Health Commissioner Androulla Vassiliou said that in her personal opinion people should "try to avoid non-essential travel" to areas where people are known to have been infected.
US President Barack Obama, in a speech to US scientists, said the cases were a cause for concern but not alarm.
He said the declaration of a public health emergency was a "precautionary tool" to ensure that all the necessary resources were available "to respond quickly and effectively".
Swine flu officially arrived in Europe on Monday, when tests confirmed that a young man in Spain and two people in Scotland - all of whom had recently returned from Mexico - had the virus. They were said to be recovering well.
WHO PANDEMIC ALERT PHASES
Phase 1: No viruses circulating among animals causing infections in humans
Phase 2: Animal influenza virus causes infection in humans, and is considered potential pandemic threat
Phase 3: Influenza causes sporadic cases in people, but no significant human-to-human transmission
Phase 4: Verified human-to-human transmission able to cause community-level outbreaks. Significant increase in risk of a pandemic
Phase 5: Human-to-human transmission in at least two countries. Strong signal pandemic imminent
Phase 6: Virus spreads to another country in a different region. Global pandemic under way
In Canada, six cases have been recorded at opposite ends of the country, in British Columbia and in Nova Scotia.
Tests are also being carried out on individuals or groups in New Zealand, Australia, Brazil and Israel who fell ill following travel to Mexico.
In almost all cases outside Mexico, people have been only mildly ill and have made a full recovery.
Health experts say the virus comes from the same strain that causes seasonal outbreaks in humans. But they say this newly-detected version contains genetic material from versions of flu which usually affect pigs and birds.
There is currently no vaccine for this new strain, but severe cases can be treated with antiviral medication.
The WHO is advising all countries to be vigilant for seasonally unusual flu or pneumonia-like symptoms among their populations - particularly among young healthy adults, a characteristic of past pandemics.
A number of countries in Asia, Latin America and Europe have begun screening airport passengers for symptoms, while Germany's biggest tour operator has suspended trips to Mexico.
Several countries have banned imports of raw pork and pork products from Mexico and parts of the US, although experts say there is no evidence to link exposure to pork with infection.
Shares in airlines have fallen sharply on fears about the economic impact of the outbreak.
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