We report on the observation of two neutrino-induced events which have an estimated deposited energy in the IceCube detector of 1.04 $pm$ 0.16 and 1.14 $pm$ 0.17 PeV, respectively, the highest neutrino energies observed so far. These events are consistent with fully contained particle showers induced by neutral-current $ u_{e,mu,tau}$ ($bar u_{e,mu,tau}$) or charged-current $ u_{e}$ ($bar u_{e}$) interactions within the IceCube detector. The events were discovered in a search for ultra-high energy neutrinos using data corresponding to 615.9 days effective livetime. The expected number of atmospheric background is $0.082 pm 0.004 text{(stat)}^{+0.041}_{-0.057} text{(syst)}$. The probability to observe two or more candidate events under the atmospheric background-only hypothesis is $2.9times10^{-3}$ ($2.8sigma$) taking into account the uncertainty on the expected number of background events. These two events could be a first indication of an astrophysical neutrino flux, the moderate significance, however, does not permit a definitive conclusion at this time.
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