Colombia said it would not allow any further temporary openings of the border, which Venezuela shut last year.
More than 100,000 people went to Colombia last weekend, the second time the border was open in a year.
They crossed to buy basic goods that are in short supply in their country because of a severe economic crisis.
Venezuelan President Nicolas Maduro ordered the closure to fight cross-border crime. He said the area had been infiltrated by Colombian paramilitaries and gangs.
The UN human rights office called on Venezuela to consider accepting "humanitarian aid" to ensure food and medicine supplies were distributed.
Colombia's Foreign Minister, Maria Angela Holguin, said a decision had been made to not allow any further temporary reopening of the border.
"Let's work so that the opening, the next opening, is definitive," she said after meeting officials from the region neighbouring Venezuela.
She added that work needed to be done to make the frontier safer and to prevent criminal activities in the area.
Many in Venezuela say they have struggled to feed their families as the country has suffered severe shortages for months.
This is a result of the falling price of oil which is Venezuela's prime source of income.
Supermarkets have empty shelves and people spend days in queues to buy basic goods.
The Venezuelan opposition blames the government for the economic crisis, saying its policies have left businesses unable to import raw materials and essential parts.
President Maduro argues that his leftist government is the victim of an economic war.
Expressing concern about "severe shortages" of basic goods in Venezuela, the UN human rights office also warned about deteriorating human rights and growing violence in the country.
The body urged the authorities to ensure the right to freedom of expression and peaceful assembly.
Venezuela: Economy on the brink?

The corruption allegations came in a video by opposition campaigner Alexei Navalny, viewed by millions on YouTube.
Mr Medvedev's properties include a vineyard in Italy, a mountain villa, and two luxury yachts, it is alleged.
"They pick up any old tosh, nonsense, about me or my acquaintances, and people I've never heard of," he said.
It is the first time he has commented on the claims published by Mr Navalny's anti-corruption network on 2 March.
Mr Navalny said the prime minister profited from a complex business network which concealed "bribes" by using offshore schemes and charity foundations.
The claims stirred up mass protests which saw thousands of Russians march against the government in several cities on 26 March. Hundreds of demonstrators were detained, many of them young supporters of Mr Navalny.
The following day a court jailed Mr Navalny for 15 days for disobeying a police officer.
Mr Medvedev said the "provocative" video was "expensively produced - financed by private sponsors" and "aimed at achieving a specific political result".
"They lure young people via social media, and those youths come out with certain slogans, unfortunately in violation of the law. In essence, they expose them to the machinery of law enforcement, and those youths suffer as a result."
He was speaking to workers at a bacon factory in the Tambov region, south of Moscow.
Mr Navalny - a fierce critic of President Vladimir Putin and his Kremlin associates - plans to run for the Russian presidency next year.
Mr Medvedev said he had "strong nerves" which protected him from such attacks. "If I reacted each time to such attacks I simply wouldn't manage to get on with my job as normal."
The government in Colombia has called for the permanent opening of its border with Venezuela after crisis-hit Venezuelans flocked to buy basic items.
[NEXT_CONCEPT]
Russian Prime Minister Dmitry Medvedev has dismissed as "nonsense" allegations that he has secretly accumulated a vast fortune including country estates.