We evaluate the shifts imparted to vibrational and rotational levels of a linear molecule by a nonresonant laser field at intensities of up to 10(12) W/cm(2). Both types of shift are found to be either positive or negative, depending on the initial rotational state acted upon by the field. An adiabatic field-molecule interaction imparts a rotational energy shift which is negative and exceeds the concomitant positive vibrational shift by a few orders of magnitude. The rovibrational states are thus pushed downward in such a field. A nonresonant pulsed laser field that interacts nonadiabatically with the molecule is found to impart rotational and vibrational shifts of the same order of magnitude. The nonadiabatic energy transfer occurs most readily at a pulse duration which amounts to about a tenth of the molecule's rotational period and vanishes when the sudden regime is attained for shorter pulses. We applied our treatment to the much-studied Rb-87(2) molecule in the last bound vibrational levels of its lowest singlet and triplet electronic states. Our calculations indicate that 15 and 1.5 ns laser pulses of an intensity in excess of 5 x 10(9) W/cm2 are capable of dissociating the molecule due to the vibrational shift. Lesser shifts can be used to fine-tune the rovibrational levels and thereby affect collisional resonances by the nonresonant light. The energy shifts due to laser intensities of 109 W/cm(2) may be discernible spectroscopically, with a 10 MHz resolution.