A protest is planned outside Dublin's Garden of Remembrance, a memorial to Irish people who died fighting for independence from Britain, which the queen will visit.
Ireland will mount its biggest security operation to welcome Britain's queen Elizabeth and US President Barack Obama in the space of a week.
Militant groups opposed to Britain's control of Northern Ireland are the biggest risk during the queen's four-day visit.
"We know her majesty is welcome in this country," superintendent John Gilligan told a news conference.
"Unfortunately in this country still we have a threat posed by dissident republicans," he said.
"The gardai (police) are prepared if necessary to deal with any issue that may arise."
Surveillance has been increased on suspected dissident republicans and al-Qaeda sympathisers, some of whom have been arrested and questioned. Police have sealed inspection covers in roads and combed central Dublin, where much the queen's visit will be focused.
Up to 5,000 police officers, backed by 2,000 soldiers and with support from the navy and airforce, will provide security during the monarch's engagements, which include a visit to the Guinness brewery in Dublin and a stroll around a food market in the southern city of Cork.
Gilligan said "elaborate" road closures were planned.
Adding to the security headache is the arrival of British Prime Minister David Cameron for the state dinner in the queen's honour at Dublin Castle on May 18. On the same evening, the UEFA Europa League final will be held in Dublin between Portuguese teams Porto and Benfica.
Police in Northern Ireland have sent two water cannon trucks and an armoured Land Rover used whenever the queen visits the province.
The threat from dissident nationalists in Northern Ireland is the highest since a 1998 peace deal ended a violent campaign by the Irish Republican Army (IRA).
The number of bomb attacks in Northern Ireland has doubled in the past 12 months and at a commemoration last month a masked member of one dissident group condemned the queen's visit and called on nationalists to demonstrate against it.
A protest is planned outside Dublin's Garden of Remembrance, a memorial to Irish people who died fighting for independence from Britain, which the queen will visit, as well as on the evening of the state banquet.
Three days after the departure of the queen, US President Barack Obama will arrive to meet the Irish president and prime minister and visit the Co.Offaly town of Moneygall from where one of his ancestors emigrated in the 1800s. Obama may also address a public gathering in Dublin in his May 23-24 visit.
Fears of possible revenge attacks after the killing of al-Qaeda leader Osama bin Laden has heightened the security preparations around Obama.
US secret service agents have vetted Moneygall, whose near 300 inhabitants are delighted at the prospect of welcoming their "most famous son".
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