Six weeks of red-shirt protests have severely challenged the Thai government.
It is under increased pressure to find a way out of the conflict but room for negotiation appears to be slim, correspondents say.
United Nations Secretary General Ban Ki-moon said through a spokesman that it was "a moment requiring restraint on all sides".
The protesters are occupying swathes of Bangkok's shopping hub and have built barricades, the largest of which faces police in the Silom business district.
Early on Friday, police moved across the main Rama IV road up to the red-shirt barricade for about two hours, only to pull back again.
AT THE SCENE
By Alastair Leithead, BBC News
The morning after a night marked by bomb blasts and small skirmishes began with a show of strength by riot police.
They surged forward, lining up just metres from the red-shirts' tyre, wire and sharpened bamboo-stick barricade.
The police soon withdrew, but this busy road junction on the edge of Bangkok's financial district has now become the most likely flashpoint.
Tension builds here from late afternoon, not just between the red-shirts and security forces, but with a group of anti-red shirt demonstrators who gather to hurl insults - and last night rocks and glass bottles.
It was among them the explosions went off, and where flowers were being laid this morning.
It's currently calm, but the atmosphere can change very quickly.
Protesters were hurling abuse and waving sharpened bamboo spikes - to impassive stares from the security forces.
The red-shirts later agreed to move back from their barricade by about 100m.
At least 75 people, many of them commuters on Bangkok's elevated train system, the Skytrain, are being treated in hospitals after Thursday night's attacks in Silom.
Earlier reports had said that three people were killed, but the government later said that one person died.
Deputy Prime Minister Suthep Thaugsuban said the explosions were caused by M79 grenades launched from a southern corner of Bangkok's Lumpini Park, which is behind the red-shirts' main barricade.
Government spokesman Panitan Wattanayagorn said they were "the work of the terrorists that the government has always been wanting to get rid off".
But red-shirt leaders denied all responsibility for the explosions, saying they were not in the business of hurting innocent people.
A senior police officer has announced a multi-agency investigation into the violence, as well as into the earlier failed military crackdown of 10 April that left 25 people dead.
In the business district, many shops and offices were closed as Bangkok residents chose to avoid the area.
Bangkok has been on edge for days, with the armed forces and senior government figures repeatedly issuing warnings to the red-shirt protesters to leave the centre of the city.
14 Mar: Red-shirts converge on Bangkok, hold first big rally, occupy government district
16 Mar: Protesters splash their own blood at Government House
30 Mar: A round of talks with the government ends in deadlock
3 Apr: Red-shirts occupy Bangkok shopping district
7 Apr: PM Abhisit orders state of emergency
10 Apr: Troops try to clear protesters; 25 people are killed and hundreds injured
22 Apr: Grenade blasts kill one and injure 85 near protest hub; each side blames the other
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