The number of workers on payrolls rose by 268,000 last month following a 5,000 fall in May and outstripping forecasts of a 220,000 increase.
But unemployment rose slightly to 4.3 per cent from 4.2 per cent. Average hourly earnings were up five cents or 0.4 per cent, but a 1 per cent downward revision for May made comparisons difficult.
The Dow Jones broke its previous intraday high of 11130.67 by 0.1 - the narrowest of margins - before falling back.
The market was on track to beat its previous closing high of 11107 as traders reacted euphorically to the jobs data.
The Fed changed its bias on monetary policy to neutral from "tighten" on Wednesday after raising rates by 0.25 per cent.
The shift was taken as a sign that the Fed had ruled out another hike in August.
But the minutes published on Thursday revealed the Fed was keeping a watchful eye for any signs of inflationary pressures.
Kim Rupert, of Standard & Poor's, said: "It's probably a sufficient mix to keep us waffling around with respect to what the Fed will be doing in August. It doesn't really give us a clear signal."
Michael Moran, chief economist at Daiwa Securities, said: "In terms of monetary policy, it does not show definitively that the Fed needs to tighten in the near term. It would allow the Fed to take a gradual approach to tightening."
Richard Yamarone, Senior Economist, Argus Research, said: "We're still operating at full employment. Everyone who wants a job has one. That full employment is a powerful source for consumer spending."