"If it's for security reasons, the response should not be to close the border. It rather should be to cooperate more effectively with Colombian authorities," Santos said yesterday.
Venezuela's President Nicolas Maduro however said it was good news that a meeting of the neighbors' foreign ministers had been set for Wednesday to address the row.
The border stretch will not reopen, Maduro said, "until the attack on Venezuela's economy from inside Colombia stops."
Maduro had initially closed the border for 72 hours, but on Friday he extended it indefinitely and declared a state of emergency in Tachira, a hotbed of opposition to his leftist government.
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Authorities said two assailants on a motorcycle fired on a patrol that was on a counter-smuggling mission in the town of San Antonio del Tachira, wounding three soldiers and a civilian.
Santos said the two countries had the same interest in eliminating the gangs of smugglers that operate on the border, and should work more closely together.
The Venezuelan government has blamed the smuggling of heavily subsidized food and other goods to Colombia for widespread shortages throughout the country.