Police say the gunmen who seized the two women Thursday, both logistics officers with aid group Medecins Sans Frontieres (MSF, Doctors Without Borders), were fighters from the Somali Islamist Shebab force.
"There are all indications that they are on the other side (of the border)," regional police chief Leo Nyongesa told AFP.
It was the third incident of foreigners being abducted in Kenya in just over a month.
Aid agencies said they were halting all but life-saving relief efforts in Dadaab -- home to some 450,000 mainly Somali refugees fleeing drought, famine or war -- as they reviewed the security situation.
The organisation has 49 foreign employees in the Dadaab refugee camp, including the two kidnapped Spanish women, and 343 local staff.
"The majority of foreigners were evacuated, as well as some local employees who preferred to leave," a spokeswoman for the Spanish branch of the agency said after the news conference.
The humanitarian group was still offering emergency services in the camp, but had stopped providing some medical services, it said in a statement.
However, the UN refugee agency (UNHCR) said the distribution of food, water and medical services would continue.
The kidnapping
Baston identified the two women as Montserrat Serra, 40, and Blanca Thiebaut, 30. Both had been in Kenya for about one month, he said.
Their Kenyan driver, who was shot during the kidnapping, 31-year-old Mohamed Hassan Borle, was in a stable condition at a Nairobi hospital and his life is not in danger, he added.
In a telephone conference call in Nairobi, Marthe Everard, the World Health Organisation's representative for Somalia, said the Shebab had denied having abducted the pair.
"We have here information that Al Shebab is saying that they have not done it, we have to see if this is true or not true," she said.
Fierce fighting was reported Thursday in a town just inside Somalia between Al-Qaeda linked Shebab militants and other rival Somali militia groups.
Despite the likelihood that the kidnappers are now in Somalia, police used helicopters to continue the search inside Kenya Friday.
At least three gunmen attacked the aid workers, shooting the Kenyan driver in the neck before driving off with the women, a watchman who witnessed the attack told AFP, asking not to be named.
"The two white women were playing with children near the car... then there was shooting, and people ran in all directions," he said.
Recent kidnappings
Kenya is still reeling from the recent kidnappings of a French and a British national from coastal regions, which has dealt a blow to its key tourism sector.
Kenyan authorities have on several occasions expressed fears Islamist extremists would infiltrate the Dadaab camps from Somalia, as the border lies barely 100 kilometres (60 miles) away.
Gary McGurk of Care Kenya, which is working in Dadaab, said: "All agencies have to review their security processes, because the safety of our staff is of huge importance."
Kenyan police already provide armed escorts when their staff were working, he added.
But a Kenyan driver working for Care is still missing after he was abducted in September at gunpoint at the wheel of his vehicle in Dadaab.
"There is clearly a problem, because we can't keep providing essential services if our staff are being kidnapped," McGurk added.
"But at the same time we cannot just stop those services to the half a million people who depend on them."
Refugees fear consequences
Somalis sheltering at Dadaab, which is the biggest refugee camp in the world, also fear the potential effects of the attacks.
"Our biggest fear is that we will lose services like food, water or healthcare," said one refugee, 30-year-old Yusuf Raagow Mohamed.
"The kidnappers bring here the issues we left behind in Somalia, they are people who only want to get money," said Seynab Geedi, 50.
The camps have seen a huge influx of people this year -- more than 7,500 people have arrived in the crowded complex of rag, tin and plastic huts this month alone.
The exodus has been sparked by a severe drought that has affected more than 13 million people across the Horn of Africa, hitting Somalia especially hard.
